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A ship is approaching an observation tower. If the time taken by the ship to change the angle of elevation from 30° to 45° is 10 minutes, then find the time the ship will take to cover the remaining distance and reach the observation tower assuming the ship to be travelling at a uniform speed.
  • a)
    15 minutes 20 seconds
  • b)
    13 minutes 40 seconds
  • c)
    16 minutes 40 seconds
  • d)
    Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
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A ship is approaching an observation tower. If the time taken by the s...

Let AB be the observation tower and h be its height.
Also, let the ship be at C when the angle of elevation is 30° and at D when the angle of elevation is 45°.
The time taken by the ship to travel from C to D is 10 minutes and we need to find out the time the ship will take to reach B from D.
∴ tan 30º = AB/CB = h / CB = 1/ √3
⇒ CB = √3 x h
∴ tan 45º = AB / DB = h / DB = 1
⇒ DB = h
⇒ CD = CB – DB = (√3h – h) = h(√3– 1)
Now, as h(√3 – 1) distance is covered in 10 minutes, a distance of h is covered in = 13.66 minutes = 13 minutes 40 seconds
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A ship is approaching an observation tower. If the time taken by the s...
Given Information:
- Initial angle of elevation = 30°
- Final angle of elevation = 45°
- Time taken to change angle of elevation = 10 minutes
- Ship travels at a uniform speed

Explanation:

Step 1: Calculate the time taken to cover the first part of the distance
- The ship takes 10 minutes to change the angle of elevation from 30° to 45°.
- This means the ship covers the first part of the distance in 10 minutes.

Step 2: Calculate the time taken to cover the remaining distance
- Since the ship travels at a uniform speed, the time taken to cover the remaining distance will be the same as the time taken to cover the first part of the distance.
- Therefore, the total time taken for the ship to reach the observation tower is 10 minutes (from Step 1) + 3 minutes 40 seconds (from changing the angle of elevation from 45° to 90°, which is the angle of elevation when the ship reaches the observation tower).
- Total time = 10 minutes + 3 minutes 40 seconds = 13 minutes 40 seconds
Therefore, the ship will take 13 minutes 40 seconds to cover the remaining distance and reach the observation tower. Hence, option B is the correct answer.
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A ship is approaching an observation tower. If the time taken by the ship to change the angle of elevation from 30° to 45° is 10 minutes, then find the time the ship will take to cover the remaining distance and reach the observation tower assuming the ship to be travelling at a uniform speed.a)15 minutes 20 secondsb)13 minutes 40 secondsc)16 minutes 40 secondsd)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
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